Nearest neighbor serial content addressable memory

ABSTRACT

A digital design and technique may be used to implement a Manhattan Nearest Neighbor content addressable memory function by augmenting a serial content addressable memory design with additional memory and counters for bit serially accumulating in parallel and subsequently comparing in parallel all the Manhattan distances between a serially inputted vector and all corresponding vectors resident in the CAM. Other distance measures, besides a Manhattan distance, may optionally be used in conjunction with similar techniques and designs.

FIELD OF THE INVENTION

Embodiments of the present invention pertain to a serially-addressedcontent-addressable memory to select the closest neighbor between thecontents of memory and the serially-inputted content. Nearest neighbordetermination may use a modified Manhattan distance calculation.

BACKGROUND OF THE INVENTION

Numerous examples of content addressable memories (CAMs) exist,including U.S. Pat. No. 6,999,331, granted Feb. 14, 2006 to Huang; U.S.Pat. No. 6,389,579, granted May 14, 2002 to Phillips et al.; as well asa serial CAM; U.S. Pat. No. 7,369,422 granted May 6, 2008 to Cooke. Theyall refer to providing output associated with the occurrence of datathat is equivalent to the data inputted into the CAM. Most CAMs compareall inputted bits, with all corresponding bits, in all words, in memory,in parallel. Cooke's serial CAM serially compares each inputted bit ofdata with all the corresponding bits of data in all words in memory. Thecurrent state of comparison is retained for each word as the CAMproceeds serially through all the bits in memory.

Traditionally, CAMs have been used in computer cache, virtual addresstranslation and routers, but not in more computationally intense “fuzzy”applications such as visual identification or speech recognition, bothof which require some form of best-fit selection. Furthermore,historically these types of pattern recognition applications have beencomputationally expensive and slow.

SUMMARY OF EMBODIMENTS OF THE INVENTION

This disclosure describes specific examples of augmenting the simpleparallel comparison function of a serial CAM by manipulating the orderof the serial input and the contents of the serial CAM memory tominimize the logic needed to perform parallel operations between theinput and each item in memory. More specifically, it describes ways toorganize and serially access the data within a high-density digitalmemory (e.g., static random access memory (SRAM) or dynamic randomaccess memory (DRAM) in a bit parallel fashion, for the purposes oftranslating ordered and serially inputted data into a value associatedwith a vector in the digital memory that is a nearest neighbor to theinputted vector. In one case, a Hamming distance function may be appliedto data, which may consist of a collection of Boolean attributes, and inanother case, a Manhattan distance function may be applied to vectordata, which may consist of a set of integer values.

To accomplish this, a serial CAM may be augmented to accumulate, inparallel, measures that are related to the distances between theinputted vector and every vector in the digital memory. This augmentedserial CAM may then output a value associated with the vector in memorythat has the lowest measure, which is the nearest neighbor to theinputted vector. The criterion for determining the nearest neighbor maybe a Manhattan distance metric.

The vectors in memory, like the inputted vector, may be comprised of Kn-bit integers, and may be organized in n K-bit groups, each groupcontaining one bit of equivalent significance from each integer, and theK-bit groups may be ordered from most significance to leastsignificance, allowing each integer in memory to be compared with thecorresponding inputted integer, in order, from the most significant bitto the least significant bit. The Manhattan nearest neighbor may then bedetermined by calculating the sums of the absolute values of thedifferences between the inputted vector's coordinate values and thecorresponding coordinate values of all the vectors in memory, andchoosing the smallest sum. This Manhattan distance calculation may beperformed in parallel between a properly order input vector and eachvector in memory by:

-   -   a. Comparing the corresponding coordinate values of the input        and memory vectors in order from most to least significant bit,    -   b. Saving the sign of the most significant bit of the        differences between the corresponding values of each pair of        input and memory vectors,    -   c. For each bit of significance, summing the products of the        sign from step (b) and that value's bit of difference with all        the other corresponding bits of differences, and    -   d. In order from the most to least significant bit, successively        doubling the cumulative result and adding the values from step        (c).

After the input vector has been completely serially inputted, thecumulated differences may be successively compared, one bit at a time,until one least distance remains, or until there is no differencebetween the input vector and one or more vectors in memory.

In other words, the Manhattan distance between a properly formattedinput vector and each of a set of corresponding vectors in memory, eachwith K coordinate values, may be calculated in parallel, using one K-bitcompare register, one K-bit sign register and one counter/shifter foreach word in the memory. The Manhattan nearest neighbor of anappropriately ordered input vector out of a set of similarly orderedvectors in memory may be calculated by: bit serially comparing,successively capturing the sign of the difference, accumulating thedifferences between the inputted vector and each vector in memory, andselecting the least of the calculated differences within one or moreclock cycles following loading the last bit of the input vector.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described in connection withthe attached drawings, in which:

FIG. 1 is a diagram of a serial CAM with parallel write capability,

FIG. 2 is a simplified diagram of compare logic for a word of a serialCAM,

FIG. 3 is a diagram of a slice of serial CAM compare and encode logicaugmented with additional logic for a Manhattan Nearest Neighborcalculation,

FIG. 4 is a diagram of a modified portion of the compare and encodelogic,

FIG. 5 is a diagram of an up/down/shift counter, and

FIG. 6 is a diagram of a serial nearest neighbor CAM.

DESCRIPTION OF VARIOUS EMBODIMENTS

Various embodiments of the present invention is now described withreference to FIGS. 1-6, it being appreciated that the figures illustratevarious aspects of the subject matter and may not be to scale or tomeasure.

An embodiment of the present invention may be an augmented serialcontent addressable memory comprising an orthogonal memory containingthe set of vectors to compare, comparison logic to detect one or morematches, a memory to hold intermediate sign information, and a counterfor each vector in memory to hold a portion of a distance calculationbetween the inputted vector and the corresponding vector from theorthogonal memory.

Reference is now made to FIG. 1, a diagram of a binary/ternary serialCAM with parallel write capability. In this embodiment, an orthogonalmemory core 10 includes a parallel data in port 11 for writing data intothe memory. The address lines for writing the parallel data into thememory are perpendicular to the parallel data in lines and originate inthe compare logic module 12. The bit address lines select a bit fromeach word read into the compare logic module 12, which contains comparelogic for each word that selects, from the encode logic 14, a result 16to be outputted after the data inputted via the Serial-Data In 17matches the contents in the Memory Core 10.

The Clear 15 and Write 18 signals control the addition and deletion ofdata in the Memory Core. Without altering or elaborating on the methodsto add and delete data from the Memory core, this structure may beaugmented to select the nearest neighbor of the inputted data from thepoints in memory.

Reference is now made to FIG. 2, a simplified diagram of compare logicfor a word of a serial CAM. The circular address 20 may be used toselect one bit from all the words in the orthogonal memory 10, forexample, progressing serially from the first to the last bit in memory.Each bit may be compared via an XNOR gate 21 with the bit value from theSerial Data In 17. If the values do not match, the Flip-flop 22 may thenbe reset and the AND gate 24 may function to keep it reset until the endof the compare. After the last bit has been compared, the match 13signal may then be high if at least one match has occurred, and the-valid 19 signal may be high if more than one match has occurred. If atleast one match has occurred, the AND gate 23 may select the encodelogic 14 for the first match in memory.

The CAM logic described above may be augmented to perform a nearestneighbor selection, for example, by reordering the contents of theorthogonal memory 10 and the serially inputted data into a form suitablefor parallel computation and adding additional comparison logic.

Typically, finding the nearest neighbor to a particular point in amathematical space involves evaluation of a distance metric betweenvectors representing those points. The well-known Euclidean distancebetween two points in a K-dimensional space is the square root of thesum of the squares of the differences between the coordinates in each ofthe K dimensions.

Another simpler distance metric is the Hamming distance. The Hammingdistance between a K bit logical vector in memory and a seriallyinputted K bit input vector, may be calculated by summing thedifferences between the corresponding K bits.

Yet another distance metric that is similar to, but simpler thanEuclidean distance is the Manhattan distance, which is so called becauseto get from one point to another in Manhattan, one must follow thestreets, which are laid out on an X−Y grid. The Manhattan distance isgenerally calculated by the summing the absolute values of thedifferences of the coordinates in the K-dimensional space. Thediscussion will now focus on the use of the Manhattan distance metric,and coordinates that are represented as binary integers, but it shouldbe understood that the invention is not limited to this metric orcoordinate representation and that other suitable metrics andrepresentations of coordinates may be used.

With respect to various embodiments of this invention, a ManhattanDistance measure, mathematically is the sum of the absolute values ofthe differences between the inputted vector's coordinate values and thecorresponding coordinate values of each of the vectors in memory. Theabsolute value of the difference between two binary numbers is theabsolute value of the sum of the differences of the bits ofcorresponding significance. For example, given two n-bit binary values Xand Y, the absolute value of their difference is:|(X_(n)−Y_(n))*2^(n)+(X_(n−1)−Y_(n−1))*2^(n−1) . . +(X₀−Y₀)*2⁰|.

This difference may be simplified because it is zero until bit j, thefirst bit that does not match. The difference may then be expressed as|(X_(j)−Y_(j))*2^(j) . . . +(X₀−Y₀)|; but this is equal to(X_(j)−Y_(j))*2^(j) . . . +(X₀−Y₀), if X−Y is positive, and−(X_(j)−Y_(j))*2^(j) . . . −(X₀−Y₀), if X−Y is negative. Taking this onestep further, X−Y is positive if X_(j)−Y_(j) is positive, and X−Y isnegative if X_(j)−Y_(j) is negative. So, if we call the sign of thedifference S(X−Y)=X_(j)−Y_(j) where j is the most significant bit suchthat X_(j)−Y_(j)≠0, then for memory vectors comprised of coordinatevalues X=[A, B . . . K] and the inputted vectors comprised of coordinatevalues X=[A, B . . . K], the sum of the absolute value of thedifferences may be calculated as:

$\left. {{{Manhattan}{\;}{{Distance}\left( {X,\underset{\_}{X}} \right)}} = {{\left\lbrack \;{{{\ldots\mspace{11mu}\left\lbrack {{{S\left( {A - \underset{\_}{A}} \right)}\left( {A_{j} - {\underset{\_}{A}}_{j}} \right)} + {{S\left( {B - \underset{\_}{B}} \right)}\left( {B_{j} - {\underset{\_}{B}}_{j}} \right)} + {\ldots\mspace{11mu}{S\left( {K - \underset{\_}{K}} \right)}\left( {K_{j} - {\underset{\_}{K}}_{j}} \right)}} \right\rbrack}*2} + {{S\left( {A - \underset{\_}{A}} \right)}\left( {A_{j - 1} - {\underset{\_}{A}}_{j - 1}} \right)} + {{S\left( {B - \underset{\_}{B}} \right)}\left( {B_{j - 1} - {\underset{\_}{B}}_{j - 1}} \right)} + {\ldots\mspace{11mu}{S\left( {K - \underset{\_}{K}} \right)}\left( {K_{j - 1} - {\underset{\_}{K}}_{j - 1}} \right)}} \right\rbrack*2} + {\ldots\mspace{14mu}{S\left( {A - \underset{\_}{A}} \right)}\left( {A_{0} - {\underset{\_}{A}}_{0}} \right)} + {{S\left( {B - \underset{\_}{B}} \right)}\left( {B_{0} - {\underset{\_}{B}}_{0}} \right)} + {\ldots\mspace{11mu}{S\left( {K - \underset{\_}{K}} \right)}\left( {K_{0} - {\underset{\_}{K}}_{0}} \right)}}} \right\rbrack.$

Reference is now made to FIG. 3, a diagram of serial CAM encode logic 14and compare logic 39 augmented with additional logic 30 for a ManhattanNearest Neighbor calculation, inserted between the bit comparison XNOR21 and the AND gate 24. The additional logic 30 may include a K-bitCompare register 32, a K-bit Sign register 33 and an up/down/shiftcounter 34. On each clock cycle, one bit out of the Compare register 32and one bit out of the Sign register 33 may be enabled by one of the Kcircular address lines 31, for reading and updating. After every Kcycles, the K+1 cycle may set the last address line 35 high to enableshifting the result in the counter 34.

To begin, the Reset line 36 may be used to reset the counter 34 to zero,to set the compare flip-flop 22 to one, and to set all the bits in thecompare 32 and sign 33 registers to one. Thereafter, as long as theinput data 17 matches the data from the orthogonal memory 10 the counter34 may not count. The first time a pair of bits in one of the K pairs ofvalues does not match, a zero may then be written into the compareregister 32. Thereafter the zero may be held in that location of thecompare register by the recycling AND gate 35. In this way the compareregister 32 contains the current state of the K separate comparisonsbetween the input vector and the vector in memory. The compareregister's 32 output may be used to determine whether the Signregister's 33 contents are updated or preserved, so that the signregister 33 may preserve the input value of the first mismatch only.Thereafter, the sign register may contain the sign of the difference,which may be used to instruct the counter 34 to either count up or countdown on a mismatch. When the values on the Data in 17 and from theOrthogonal Memory 10 match, the result of the XNOR 21 is one, which maybe inputted into the -count input of the counter 34 so that the counterdoesn't count. Prior to the beginning of the next K cycles, whichcorresponds to the bits of next lowest significance with respect to thecurrent bits (i.e., corresponding to a value of half the valuerepresented by the current bits), the existing difference may bemultiplied by 2. This is accomplished on every K+1 clock cycle when theK+1 circular address line 35 is set high, which may be used to cause asingle shift in the counter 34. In this manner, the entire differencemay be accumulated over N(K+1) cycles. Thereafter, until either a singlematch occurs or all counters 34 are zero, the counters' 34 bits may beshifted out in successive cycles while the finish line 37 is high. Aseach counter 34 shifts out a high value (-Out 38 goes low), the compareflip-flop 22 may be reset, until only one flip-flop remains set. Thisflip-flop may then mark the location of the contents in the Orthogonalmemory 10 that may have the smallest Manhattan distance from theinputted vector.

Reference is now made to FIG. 4, a simplified diagram of modifiedcompare and encode logic. The encode logic 14 may be comprised ofmultiple pre-charged result lines 46, which may be pulled down byselected transistors 44, whose gate inputs 45 may be connected to aselect line 47, which may be enabled by an AND gate 42, which may serveto ensure that only the first location of a set of matching locationswill be selected. The compare flip-flop 22 may be used to hold thecompare status.

Reference is now made to FIG. 5, a diagram of the up/down/shift counter.The counter 34 may have multiple single bit stages 50 that may beconnected to form a counter with the ability to shift, increment ordecrement. When the Up/Dn input 55 is high, it may then controlmultiplexors 53 to select the positive count, and it may controlmultiplexors 53 to select the negative count if the Up/Dn input is low.When the -count input 57 is low, the count in the counter 34 may beincremented or decremented based on the state of the Up/Dn input 55.When shift is high, it may control multiplexors 54 that select the zero52 and the contents of the prior flip-flop, and through OR gates 51, mayenable clocking of all the stages of the counter 34 to double the count.if the counter overflows, the -Out signal 59 may then go low. The resetsignal 58 may be used to clear the count in the counter 34.

Given that the vectors in memory may be K n-bit unsigned integer values,the worst-case difference would be K*2^(n+1)−K, which can be kept in acounter that is (N+log₂(K)+2) bits in size, but in another embodiment ofthe present invention, the size of the counter may be as small aslog₂(K)+2 bits, regardless of the size of the integer coefficients.

Reference is again made to FIG. 3, a diagram of a slice of serial CAMcompare logic augmented with additional logic for a Manhattan NearestNeighbor calculation. The counter's 34 -out signal 38 may go low if thecounter 34 overflows, which may, in turn, clear the compare flip-flop22. In other words, the compare flip-flop 22 may hold the comparison ofthe differences above what is held in the counters 34, so it may bepossible for the counters to be only large enough to ensure that theminimum difference is selected.

To find the smallest counter, one may look at the intermediatedifference calculation. The largest count for a bit group is K, whichmay be doubled before adding or subtracting the next-lower significancebits, so the largest and smallest values that a cumulative count of Kcan be after another cycle are 3K and K. Now, after another cycle, thelargest and smallest 3K can become are 7K and 5K, and K can become (asbefore) 3K or K. So the elimination, on each cycle, of any differenceabove 2K would still preserve the minimum because no intermediatedifference, once doubled to 4K, will ever reduce below 2K. A count of 2Kcan be contained in a counter of log₂(K)+2 bits. Furthermore,subtracting the same constant from a set of remaining differences doesnot change the order of those differences.

Reference is again made to FIG. 4, a diagram of a modified portion ofthe compare and encode logic. Unlike a CAM, which may not contain amatch to the inputted vector, there is always at least one nearestneighbor to the inputted vector, and yet the possibility exists that atany time the counter 34 shifts, all the matching words may beeliminated. This can occur if all words that have a positive comparestatus have their counters 34 overflow, setting their -Out signals 38low, on the same cycle. If this occurred, without correction, all thecompare flip-flops 22 would reset, no match would occur, and the minimumdifference would be lost. This condition may be possible if all thedifferences that have not yet overflowed were to overflow at the sametime. This may be avoided by including a -no match line 40, which may bepulled down by an N-channel transistor 41 if the compare status 43 ishigh. On the other hand, if all matches have been eliminated, all thecompare status lines 43 may then be low, and the -no match line 40 maystay high, which may thus disable the compare flip-flops 22 and thuspreserve their compare status values for the next cycle. This isequivalent to subtracting a constant from each of the remainingdifferences, which as stated above, may preserve the minimum selectioncalculation.

In other words, in yet another embodiment of the present invention thelocation of the minimum of a set of numbers, residing in memory, eachwith a corresponding flag, also in memory, may be found by selecting aninteger m such that the maximum of the set of numbers is less than2^(m), setting the flags of all the numbers, and performing thefollowing until all numbers are zero:

-   a) double all the numbers;-   b) if any number, with a flag that is set, is less than 2^(m), then    clear the flags of all numbers greater than 2^(m)−1; and-   c) subtract 2^(m) from all the numbers.    The location of a minimum may then be selected from the locations    with flags that are still set.

Reference is now made to FIG. 6, a diagram of a serial nearest neighborCAM. For K n-bit integer vectors, Manhattan nearest neighborcalculations may be performed in n(K+1) cycles, and the nearestneighbors may be selected in another log₂(K)+2 clock cycles after that.In addition, one initial clock cycle may be used to reset the logic. Thereset signal 64 may set the circular address shift registers 65 and 67to their first addresses and may reset the comparison logic 68 and theLog K Counter 62. For the next n(K+1) cycles, the main circular addressshift register 66 may shift through the KN address lines to the MemoryCore 10. After each group of K bits, the K+ circular address shiftregister 67 may enable a K+1 address, which may shift the differences ineach of the counters, effectively doubling the differences, and maydisable the Main circular address shift register 66 with a disablesignal 65 for that single cycle. After the last bit line in the MemoryCore 10 has been accessed, the Main circular shift register 66 mayenable an NK+1 line 69, which may enable the Log K Counter 62, which maythen count to log₂(K)+2 and may roll over. The finish signal 37 may bedesigned to remain high as long as the count in the Log K counter is notzero. If there is more than one matching location when the Log K Counter62 rolls over, the results from the first of the closest remainingnearest neighbors may be outputted on the result signals 16; however,the invention is not thus limited, and other criteria may be used forselecting which of the closest remaining nearest neighbors may beoutputted.

Reference is now made to FIG. 4, a diagram of a modified portion of thecompare and encode logic. Since log₂(K)+2 shift cycles may occur afterthe last difference may have been incremented or decremented, theremaining values in the counters 34 may have been completely shiftedout. If the compare flip-flop 22 is not cleared before the last shiftcycle, subsequent cycles of shifting while the input and memory bits areequal may not affect the compare flip-flops 22. If multiple locationshad the same minimum distance, the AND gate 42 may enable only the firstselect line 47.

From this it can be seen that a Manhattan Nearest Neighbor selectionbetween an input vector consisting of K n-bit integers and a set ofsimilarly constructed vectors in memory may be performed in no more thann(K+1)+log₂(K)+3 cycles, regardless of how many vectors reside inmemory.

Now in yet another simplified embodiment of the present invention, theorthogonal memory may be comprised of K 1-bit logical elements, eachrepresenting the logical presence or absence of a characteristic of anobject represented by the K bit word. Serially inputting a similar inputvector to the serial nearest neighbor CAM shown in FIG. 6, may result inchoosing the nearest Hamming Distance neighbor after no more than K+log2(K)+4 clock cycles, because the nearest neighbor CAM may then count thenumber of differences between the K elements in memory and the Kinputted elements and then select the resulting minimum count. It isalso understood that a custom implementation for selecting the nearestneighbor solely based on a Hamming Distance metric may not require thecompare or sign memories.

It will be appreciated by persons skilled in the art that the presentinvention is not limited by what has been particularly shown anddescribed hereinabove. Rather the scope of the present inventionincludes both combinations and sub-combinations of various featuresdescribed hereinabove as well as modifications and variations whichwould occur to persons skilled in the art upon reading the foregoingdescription and which are not in the prior art.

1. A digital logic device comprising: a serial data input to the digitallogic device; a first memory circuit; and compare logic circuitry forrespective words of said first memory circuit. wherein the compare logiccircuitry for a respective, word of the first memory circuit isconfigured to serially accept each of all bits of the respective wordand to serially compare each serially accepted bit from the respectiveword with a bit of serial data from the serial data input, and whereinthe compare logic circuitry is configured to perform the serialcomparing for the respective words of the first memory circuit inparallel.
 2. The digital logic device as in claim 1, wherein saidcompare logic circuitry includes a shifter/counter to accumulate thecomparison results.
 3. The digital logic device as in claim 1, whereinthe digital logic device is configured to perform said comparison andcalculating the distance metric in parallel for words stored in thefirst memory circuit, and to perform this parallel comparison andcalculating serially, for respective bits as they are input through theserial data input.
 4. The digital logic device as in claim 1, whereinthe digital logic device is configured to traverse the words stored inthe first memory circuit in parallel, from most-significant bit (MSB) toleast-significant bit (LSB), and to set a sign of the distance metricfor a given word based on a first bit of the given word that fails tomatch a bit from the serial data input
 5. The digital logic device as inclaim 1, further comprising; a second memory circuit; wherein saidsecond memory circuit is configured to contain information related tosaid serial comparison, and wherein said compare logic is configured toincrementally calculate a distance metric between the respective wordand the bits of said serial data input, using said information relatedto said serial comparison.
 6. The digital logic device as in claim 5,wherein said compare logic circuitry includes shifter/counter logicconfigured to perform one or more operations based at least in part onat least a portion of said information related to the comparison.
 7. Thedigital logic device as in claim 5, wherein said distance metric is aHamming distance metric.
 8. The digital logic, device as in claim 5,wherein said distance metric is a Manhattan distance metric.
 9. Adigital logic device comprising: a serial input to the digital logicdevice; at least one memory circuit containing at least one set ofitems; logic circuitry configured to perform operations ID parallelbetween data from said serial input and at least a subset of said set ofitems from at least one said memory circuit, the subset containing atleast two items of said set of items, wherein the logic, circuitry isfurther configured to accept in parallel data of said at least a subsetof said set of items to serially receive data from the serial input andto perform the parallel operations as the data from the serial input areserially received, wherein the parallel operations are performed on acommon item data received from the serial input in parallel withparallel data items of said at least a subset of said set of items:wherein said logic circuitry is further configured based on a serialordering used to order data inputted into said serial input.
 10. Thedigital logic device as in claim 9, wherein an input vector to the logiccircuitry is ordered into groups of bits, one bit from each coordinateof an item associated with said set of items, in order from most toleast significant bit.
 11. The digital logic device as in claim 9,wherein said items in said set of items are ordered into groups of bits,one bit from each coordinate of an item, in order from most to leastsignificant bit.
 12. A digital logic device comprising: a serial daminput to the digital logic device; a serial content-addressable memory(CAM) circuit; a second memory circuit; and compare logic circuitry foreach word of said serial CAM circuit; wherein said second memory circuitis configured to contain information reflecting a result of a comparisonof a portion of data from said serial CAM and said serial data input,and wherein said compare logic circuitry incrementally calculates adistance metric between said data from said serial CAM and said serialdata input, using said information reflecting the result the comparison.13. The digital logic device as in claim 12, wherein said compare logiccircuitry includes shifter/counter logic configured to perform one ormore operations based at least in part on at least a portion of saidinformation reflecting the result of the comparison.
 14. The digitallogic device as in claim 13, wherein said distance metric is a Hammingdistance metric.
 15. The digital logic device as in claim 12, whereinsaid compare logic circuitry includes as shifter/counter to accumulatethe results of comparisons.
 16. The digital logic device as in claim 15,wherein said distance metric is a Manhattan distance metric.
 17. Adigital logic device comprising: a serial input to the digital logicdevice; a serial content-addressable memory (CAM) containing at leastone set of items; logic circuitry configured to perform operations inparallel between data from said serial input and at least a subset ofsaid set of items from a serial CAM and further configured based on aserial ordering used to order.
 18. The digital logic device as in claim17, wherein an input vector to the logic circuitry is ordered intogroups of bits, one bit from each coordinate of an item associated withsaid set of items, in order from most to least significant bit.
 19. Thedigital logic device as in claim 17, wherein said items in said set ofitems are ordered into groups of bits, one bit from each coordinate ofan item, in order from most to least significant bit.